Photonic Band Gap Materials:

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Photonic Band Gap Materials The Semiconductors
of the future?
C. M. Soukoulis Ames Lab. and Physics Dept. Iowa
State University. and Research Center of Crete,
FORTH - Heraklion, Crete
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Collaborators

• Ames Laboratory, Iowa State University
• Mike Sigalas (Agilent)
• Gary Tuttle, W. Leung
• Ekmel Ozbay (Turkey)
• Rana Biswas
• Mario Agio (Pavia), P. Markos (Slovakia)
• E. Lidorikis (MIT), S. Foteinopoulou
• C.T. Chan (Hong-Kong)
• K.M. Ho
• Research Center of Crete
• E. N. Economou
• G. Kiriakidis, N. Katsarakis, M. Kafesaki
• PCIC

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Computational Methods

• Plane wave expansion method (PWE)
• C.T. Chan, K.M. Ho, E. Lidorikis, S.
  Foteinopoulou
• Transfer matrix method (TMM)
• M. Sigalas, I. El-Kady, P. Markos, S.
  Foteinopoulou
• Finite-difference-time-domain-method (FDTD)
• M. Agio, M. Kafesaki, E. Lidorikis, S.
  Foteinopoulou

soukoulis_at_ameslab.gov soukouli_at_iesl.forth.gr
http//cmpweb.ameslab.gov/personnel/soukoulis
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PHOTONIC BAND GAP STRUCTURES THE
SEMICONDUCTORS OF THE FUTURE?
PBG Crystals Periodic variation of dielectric
constant Length scale ? Man-made
structures Control e.m. wave propagation 1990s
optical fibers, lasers, PBGs --gt photonics era
Semiconductors Periodic crystal
potential Atomic length scales Crystal
structure given by nature Control electron
flow 1950s electronic revolution
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Fermis Golden Rule
hv
Density of final states
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Applications Microwaves
Dielectric
Photonic Crystal
Efficient planar antennas
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Applications Optical range
Suppression of spontaneous emission
Low-threshold lasers, single-mode LEDs, mirrors,
optical filters
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APPLICATIONS OF PBG MATERIALS

• Frequency-selective, loss-less reflection
• Filters, switches, optical amplifiers
• Areas impacted
• Automotive electronics - e.g.,
  collision-avoidance
• radar (60-77 GHz)
• Electron cyclotron resonance heating for fusion
  plasma,
• diagnostic tool (60-200 GHz)
• Medical and biological application - e.g.,
  microwave
• resonance therapy (40-80 GHz), imaging
• Wide bandwidth communication (60, 94 GHz)
• mm waveguides
• Fast electronics - interchip communication
• Remote sensing - e.g., monitoring atmospheric
  radiation
• observational astronomy
• Lasers and optical devices - improved
  performance in
• efficiency and reduction of background noise
• Photocatalysis

mm wave
Infra-red
visible
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Outline

• Progress in fabricating 3D photonic crystals
• Layer-by-Layer structure (ISU)
• 3-cylinder structure (LIGA)
• Inverse opals and ordered silica matrices (many
  groups)
• Metallic photonic crystals
• Metallic and dielectric bends
• Photonic Crystal Waveguides and Bends (2D slabs
  or 3D PCs)
• Studies of the losses and effects of disorder

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Three - cylinder Structure or Yablonovite
E. Yablonovitch
Diamond like symmetry. PRL 65, 3152 (1990) and
Euro. Phys. Lett. 16, 563 (1991)
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3-cylinder structure

E. Yablonovitch et. al. PRL 67, 3380 (1991)
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Fabrication of 3-cylinder structure by LIGA
technique
ISU, FORTH and Mainz
Appl. Phys. Lett. 71, 1441 (1997)
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experiment
v2.4 THz
Appl. Phys. Lett. 71, 1441 (1997)
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Diamond lattice gives the largest photonic band
gap
Ho, Chan and Soukoulis, PRL 65, 3152 (1990)
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Diamond lattice
Ho, Chan and Soukoulis, PRL 65, 3152 (1990)
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Photonic band gap formation
A synergetic interplay between microscopic (Mie)
and macroscopic (Bragg) resonances.
d
eo
r
ei
Bragg scattering 2d ml?????? w?/c m p / d,
m1,2,
Mie resonance 2r/li (m1)/2, m0,1,2,
Maximum reflection (m0)

Gap appears when
(filling ratio)
?
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Experimental band structure of a fcc lattice of
air spheres
Fcc Airball(86) n3.5
Gap
Yablonovitch Gmitter, PRL 63, 1950 (1989)
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FCC lattice has only a pseudogap
Ho, Chan and Soukoulis, PRL 65, 3152 (1990)
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Density of States for a fcc structure of air
spheres
figure
Ho, Chan and Soukoulis, PRL 65, 3152
(1990) Sozuer, Haus and Inguva, PRB 45, 13962
(1992) v Busch and John, PRE 58, 3896 (1998)
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Band structure for a close-packed fcc lattice of
air spheres in silicon

Busch and John, PRE 58, 3896 (1998)
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DOS for a close-packed fcc lattice of air spheres
in silicon

Busch and John, PRE 58, 3896 (1998)
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Air Spheres (e1) in Dielectric (e10) fcc
arrangement with Air filling ratio
74 supercell 3?3?3, k-point sampling 8?8?8,
total grids 72?72?72
Disorder In Position
DOS
wa/2pc
Lidorikis, Soukoulis
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Air Spheres (e1) in Dielectric (e10) fcc
arrangement with Air filling ratio
74 supercell 3?3?3, k-point sampling 8?8?8,
total grids 72?72?72
Disorder In Radius
ltrmsgt Average rms error in dielectric const.
Dv D(V/V0)
ltrmsgt Dv
DOS
wa/2pc
Lidorikis, Soukoulis
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Carbon structures with 3d periodicity at optical
wavelengths
A. Zakhidov et. al. Science, 282, 897(1998)
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On-chip natural asembly of silicon photonic
bandgap structures
Y. A. Vlasov et. al. Nature, 414, 289 (2001)
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Inversed opals infiltrated by liquid crystals
K. Busch and S. John, PRL 83, 967 (1999)
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Silicon inverted opals
A. Blanco et. al. Nature 405, 437 (2002)
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Fabrication of photonic crystals by holographic
lithography
M.Campell et. al. Nature, 404, 53 (2000)
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An easy-to-build structure with a full photonic
band gap
Iowa State layer-by-layer structure Science News
144, 199 (1993) Solid State Comm. 89, 413
(1994) Phys. Rev. B 50, 1945 (1994)
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Iowa State Universitys layer-by-layer structure
Diameter of Rods Spacing of Rods Midgap Frequency Corresponding Wavelenth at Midgap
0.32 cm 1.120 cm 13 GHz 23 mm v
0.20 cm 0.711 cm 20 GHz 15 mm v
0.08 cm 0.284 cm 50 GHz 6 mm v
340 micron 1275 micron 100 GHz 3 mm v
100 micron 350 micron 450 GHz 0.66 mm v
1.33 micron 4.74 30 THz 10 micron
0.20 micron 0.711 2 x 1014 Hz 1.5 micron
667 Å 2370 Å 6 x 1014 Hz 5000 Å
!!

!!!
?
??
Science News 144, 199 (1993) Solid State Comm.
89, 413 (1994) Phys. Rev. B 50, 1945 (1994)
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Iowa State Universitys layer-by-layer structure
Sandia National Laboratory.
Iowa State University Ames Laboratory
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Electro magnetic waves are incident on the side
surface
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Theory and experiment is in excellent agreement
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An average attenuation of 16 dB per unit cell is
obtained
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Theoretical (dashed line) and experimental (solid
line) transmission characteristics of the defect
structure
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The ISU layer by layer structure fabricated at
Kyoto Univ.
S. Noda et. al. Science, 289, 604 (2000)
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S. Noda et. al. Science, 289, 604 (2000)
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S. Y. Lin et. al. Nature, 394, 251 (1998)
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R. Biswas, ISU
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Propagation along 90 bends in 3d dielectric
structures
S. Noda, Kyoto Univ.
M. Sigalas et. al. Microwave Opt. Techn. Lett.
23, 56 (1999)
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Metallic Structure
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Metallic Structure
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Propagation along 90 bends in 3d metallic
structures
Transmission along the bend is more than 95 !!
M. Sigalas et. al. Phys. Rev. B 60, 4426 (1999)
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Agio and Soukoulis, PRE, 64, 055603R (2001)
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Waveguide modes for widths of W1 and W3
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Guided bends in Photonic Crystals - Study of
60o bends in W3 and W5 --Best the
smoothest one in collaboration with PCIC
groups
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W3 taperslit double bends
Field profile for a/l0.24
Modal analysis for slit2
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Studies of the out of plane losses
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Photonic Crystal Slabs
Kafesaki, Agio, Soukoulis, JOSA B (2002)
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Comparison of 2D and 3D results
3D
2D
3D results can be derived by an effective 2D
system with a slightly different f and an
imaginary e
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2D and 3D gaps almost coincide in position and
width.
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Y-Splitters
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Summary and Conclusions

• The layer-by-layer structure has been fabricated
  at telecom frequencies
• Inverse closed packed structures with high index
  materials (TiO2, Si, Ge)
• Doping of PBGs with active atoms and molecules
  will lead to new
• frontiers in microlasers, low threshold
  switches, random lasers
• Metallic PBGs. Connectivity is very important
• Photonic Crystal Waveguides and Bends (3d
  structures or dielectric slabs)
• Tunable PBGs
• Detailed studies of disorder are very important

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Summary

• The photon band structure problem is solved
• Photonic gaps EXIST in diamond like structures
• Structure is optimized to give largest gap
• Localization of light in imminent

Experimental Challenge
Fabricate these new dielectric structures at
optical wavelengths, then Applications of
photonic gaps in physics and engineering may
become possible.